Reassignment of magic numbers for icosahedral Au clusters: 310, 564, 928 and 1426

Icosahedral Au clusters with three and four shells of atoms are found to deviate significantly from the commonly assumed Mackay structures. By introducing additional atoms in the surface shell and creating a vacancy in the center of the cluster, the calculated energy per atom can be lowered significantly, according to several different descriptions of the interatomic interaction. Analogous icosahedral structures with five and six shells of atoms are generated using the same structural motifs and are similarly found to be more stable than Mackay icosahedra. The lowest energy per atom obtained here is for clusters containing 310, 564, 928 and 1426 atoms, as compared with the commonly assumed magic numbers of 309, 561, 923 and 1415. Some of the vertices in the optimized clusters have a hexagonal ring of atoms, rather than a pentagon, with the vertex atom missing. An inner shell atom in some cases moves outwards by more than an angstrom ngstrom into the surface shell at such a vertex site. This feature, as well as the wide distribution of nearest-neighbor distances in the surface layer, can strongly influence the properties of icosahedral clusters, for example catalytic activity. The structural optimization is initially carried out using the GOUST method with atomic forces estimated with the EMT empirical potential function, but the atomic coordinates are then refined by minimization using electron density functional theory (DFT) or Gaussian approximation potential (GAP). A single energy barrier is found to separate the Mackay icosahedron from a lower energy structure where a string of atoms moves outwards in a concerted manner from the center so as to create a central vacancy while placing an additional atom in the surface shell.

Automated summary

This study reveals that icosahedral Au clusters with three and four shells of atoms deviate significantly from commonly assumed Mackay structures. The introduction of additional atoms in the surface shell and a vacancy in the cluster's center can significantly lower the energy per atom. Similar icosahedral structures with five and six shells of atoms are also found to be more stable than Mackay icosahedra. The optimized clusters exhibit hexagonal rings at some vertices and inner shell atoms moving outward into the surface shell, which can strongly influence the properties of these clusters.